Surfaces having geometric patterns are used in a variety of applications. Generally, a laser, chemical, or other means etches geometric patterns on a surface of solid materials, such as silicon, metal, and the like, for example, as described in U.S. Pat. No. 5,888,846. Geometric patterns may be used for creating optical disk storage systems, semi-conductor chips, and photo mask manufacturing, as described in U.S. Pat. No. 5,503,963. Surfaces capable of enhancing the passage of electrons through a potential energy barrier on the border between a solid body and a vacuum, such as those described in U.S. Pat. Nos. 6,281,514 and 6,117,344, should have patterns of the dimensions of 5–10 nm.
Recent development of such technologies as electron beam milling and ion beam lithography enable the fabrication of structures with dimension as small as a few nanometers. Those low dimensions are comparable with the de Broglie wavelength of a free electron inside the metal. Because of this, it has become possible to fabricate some microelectronic devices working from the wave properties of the electrons [N. Tsukada, A. D. Wieck, and K. Ploog “Proposal of Novel Electron Wave Coupled Devices” Appl. Phys. Lett. 56 (25), p. 2527, (1990); D. V. Averin and K. K. Likharev, in Mesoscopic in Solids, edited by B. L. Al'tshuler, P. A. Webb (Elsevier, Amsterdam, 1991)].
The general case of an elementary particle in the potential energy box is depicted in FIG. 1. The behavior of a particle in the ordinary potential energy box (OPEB) is well known. The Schroedinger equation for particle wave function inside the OPEB has form [L. D. Landau and E. M. Lifshits “Quantum Mechanics” (Russian), Moscow 1963.]:d2ψ/dx2+(8π2m/h2)Eψ=0   (1)
Here ψ is the wave function of the particle, m is the mass of the particle, h is Planck's constant, and E is the energy of the particle. Equation (1) is written for the one dimensional case. General solution of (1) is given in the form of two plane waves moving in directions X and −X:ψ(x)=Aexp(ikx)+Bexp(−ikx)  (2)
here A and B are constants and k is the wave vector:k=[(2mE)1/2]/(h/2π)  (3)
It is well known that in the case of U=∞, the solution for equation (1) is defined by the boundary condition ψ=0 outside the OPEB as follows:ψ=Csin(kx)  (4)
Here C is a constant. If the width of the OPEB is L, then the boundary conditions ψ(0)=0 and ψ(L)=0 will give the solution to Schroedinger's equation in the form of sin(kL)=0, and kL=nπ(n=1, 2, 3, . . . ). This gives a well-known discrete series of possible wave vectors corresponding to possible quantum states:kn=nπ/L  (5)
and according to (3) discrete series of possible energies En=n2(h2/8mL2)
A disadvantage of e-beam or ion beam milling is that the distribution of intensity inside the beam is not uniform, which means that structures produced using these methods do not have a uniform shape. In particular, the edges of the milled areas are always rounded, repeating the shape of intensity distribution inside the beam. Such rounding is more or less acceptable depending on the type of device fabricated. However, for devices working on the basis of wave interference this type of rounding is less acceptable, because wave interference depends greatly both on the dimensions and the shape of the structure.